An investigation of the edge luminescence due to free excitons in KI and RbI has been made on bulk crystals and thin crystal plates of thicknesses from 10 to 0.1 \ensuremath{\mu}m at 11 K. In the thin samples, it is found that the edge luminescence line appears just around the absorption band attributed to the strain-induced spin-triplet states, both peaks showing the same thickness-dependent energy shift. From a close connection of these results with those obtained in unstrained bulk materials, the polariton model including the symmetry-breaking effect due to a finite exciton wave vector is invoked to account for the origin of the edge luminescence in alkali iodides. On the basis of the above arguments, the exchange energy \ensuremath{\Delta} and the spin-orbit splitting \ensuremath{\lambda} of excitons are evaluated; \ensuremath{\Delta}=20 meV and \ensuremath{\lambda}=0.89 eV for KI and \ensuremath{\Delta}=26 meV and \ensuremath{\lambda}=0.78 eV for RbI.